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Contract No. DE-AC36-08GO28308

Appending High-Resolution 

Elevation Data to GPS Speed 

Traces for Vehicle Energy 

Modeling and Simulation

E. Wood, E. Burton, A. Duran, and J. Gonder 

Technical Report

NREL/TP-5400-61109

June 2014
NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO 80401

303-275-3000 • www.nrel.gov

Appending High-Resolution 

Elevation Data to GPS Speed 

Traces for Vehicle Energy 

Modeling and Simulation 

E. Wood, E. Burton, A. Duran, and J. Gonder

Prepared under Task No. VTP2.2300

Technical Report

NREL/TP-5400-61109

June 2014
NOTICE

This report was prepared as an account of work sponsored by an agency of the United States government. 

Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, 

express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of 

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trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, 

or favoring by the United States government or any agency thereof. The views and opinions of authors expressed 

herein do not necessarily state or reflect those of the United States government or any agency thereof.

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Cover Photos: (left to right) photo by Pat Corkery, NREL 16416, photo from SunEdison, NREL 17423, photo by Pat Corkery, NREL 

16560, photo by Dennis Schroeder, NREL 17613, photo by Dean Armstrong, NREL 17436, photo by Pat Corkery, NREL 17721.

 Printed on paper containing at least 50% wastepaper, including 10% post consumer waste.
iii

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Acknowledgments

This research has been jointly supported by the U.S. Department of Energy’s Vehicle 

Technologies Office and by the U.S. Department of Transportation’s Federal Highway 

Administration. The authors would specifically like to thank Lee Slezak and David Anderson of 

the U.S. Department of Energy and Elaine Murakami of the U.S. Department of Transportation 

for their guidance and support. A special thanks to Sean Lopp of the National Renewable Energy 

Laboratory for contributing his statistical insight to this effort.
iv

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List of Acronyms

ADAS Advanced Driver Assistance Systems

DEM digital elevation model 

GPS global positioning system 

NREL National Renewable Energy Laboratory 

USGS United States Geological Survey 
v 

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Executive Summary

Accurate and reliable global positioning system (GPS)-based vehicle use data are highly valuable 

for many transportation, analysis, and automotive considerations. Model-based design, realworld fuel economy analysis, and the growing field of autonomous and connected technologies 

(including predictive powertrain control and self-driving cars) all have a vested interest in highfidelity estimation of powertrain loads and vehicle usage profiles. Unfortunately, road grade can 

be a difficult property to extract from GPS data with consistency. 

In this report, we present a methodology for appending high-resolution elevation data to GPS 

speed traces via a static digital elevation model. Anomalous data points in the digital elevation 

model are addressed during a filtration/smoothing routine, resulting in an elevation profile that 

can be used to calculate road grade. This process is evaluated against a large, commercially 

available height/slope dataset from the Navteq/Nokia/HERE Advanced Driver Assistance 

Systems product. Results will show good agreement with the Advanced Driver Assistance 

Systems data in the ability to estimate road grade between any two consecutive points in the 

contiguous United States.
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Table of Contents

List of Figures ........................................................................................................................................... vii

List of Tables ............................................................................................................................................. vii

1 Introduction........................................................................................................................................... 1

2 Methodology ......................................................................................................................................... 2

2.1 Elevation Lookup .......................................................................................................................... 2

2.2 Data Filtration ............................................................................................................................... 4

3 Validation............................................................................................................................................... 7

3.1 Example Roadway......................................................................................................................... 7

3.2 Aggregate Comparisons................................................................................................................ 8

4 Summary ............................................................................................................................................. 13

References................................................................................................................................................. 14
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List of Figures

Figure 1. Elevation map of the contiguous United States produced using the USGS DEM ............... 2

Figure 2. Elevation map of the state of Colorado produced using the USGS DEM ............................. 3

Figure 3. Coincident maps of downtown Denver, Colorado, produced using the USGS DEM, 

Google Maps Satellite layer, Google Maps Streets layer, and Google Maps Hybrid 

layer......................................................................................................................................... 4

Figure 4. Raw versus filtered USGS elevation and road grade data ..................................................... 6

Figure 5. Sample elevation and road grade (absolute value) signals with filtered USGS data plotted 

as a red line and ADAS height/slope data overlaid as blue markers................................ 8

Figure 6. Cumulative distribution of road grade by functional class .................................................... 9

Figure 7. Cumulative distribution of road grade by geography........................................................... 10

Figure 8. Distribution of road grade estimation error by ADAS road grade for Functional Class 1 

roads...................................................................................................................................... 12

List of Tables

Table 1. Step-by-Step Example of Elevation Filtration/Smoothing Performed on Sample Roadway 5

Table 2. Navteq-Defined Road Functional Classes and Descriptions................................................... 9
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1 Introduction

Accurate and reliable global positioning system (GPS)-based vehicle use data are highly valuable 

for many transportation, analysis, and automotive considerations. Model-based design, realworld fuel economy analysis and the growing field of autonomous and connected vehicle 

technologies (including predictive powertrain control and self-driving cars) all have a vested 

interest in high-fidelity estimation of powertrain loads and vehicle usage profiles [1–17]. 

Unfortunately, road grade can be a difficult property to extract from GPS data with consistency. 

While most GPS datasets do not contain explicit measurements of road grade, elevation is often 

estimated and can be used to calculate differentials for road grade estimates. However, 

depending on the distance between points, differential elevation must be measured with 

extremely high accuracy to produce grade estimates within reasonable error bounds (e.g., to 

measure road grade between points 100 m apart to within an absolute difference of ±0.1%, 

differential elevation must be accurate to within 0.1 m). While the two-dimensional accuracy of

modern GPS devices (latitude/longitude coordinates) of plus or minus a few meters is generally 

acceptable for most applications, a far higher level of accuracy is required for elevation 

measurements to produce stable road grade values.

Modern GPS devices make estimates of elevation using similar triangulation techniques to those 

underlying two-dimensional coordinate readings. However, the accuracy of GPS-estimated 

elevation can vary by up to twice as much as two-dimensional estimates due to insufficient 

positioning and availability of the satellite network [18]. Compounded by the absence of 

standardization with respect to GPS elevation measurement protocols, road grade calculation 

directly from GPS-measured elevation is fraught with complications. References [19–21] 

provide additional documentation on GPS measurement techniques and quantified error 

statistics.

Several real-time techniques for estimating road grade independent of GPS-measured elevation 

have been validated and documented in the literature, including the use of: 

• Kalman filters integrated with powertrain models and signals from the controller area 

network bus to simultaneously estimate vehicle mass and road grade [22–24] 

• Filtered differential GPS velocity signals used as vectors to directly calculate 

instantaneous road grade (potentially requiring multiple runs over a given segment for 

estimates to converge) [25–30] 

• Lidar units to measure differential elevation and distance, which are filtered and used to 

calculate the grade of the approaching roadway [31]. 

Unfortunately, these techniques are not applicable when attempting to append road grade to an 

existing database of two-dimensional GPS coordinates. Such a situation requires a reliable thirdparty dataset be employed to append the additional parameter of road grade to a GPS dataset. 

We present a methodology for appending high-resolution elevation data to GPS speed traces via 

a digital elevation model (DEM). The use of a DEM is advantageous in that it provides defined 

static elevation values that enable consistency to be maintained between different GPS datasets 

and allows for elevation/grade values to be appended to data where GPS-measured elevation is 
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unavailable. Anomalous data points in the DEM are addressed during a filtration/smoothing 

routine, resulting in an elevation profile that can be used to calculate road grade. This process is 

evaluated against a large, commercially available height/slope dataset from the Navteq/Nokia/ 

HERE Advanced Driver Assistance Systems (ADAS) product. Results show good agreement 

with the ADAS data in the ability to estimate grade at any arbitrary point in the contiguous 

United States, including on all freeway, arterial, collector, and local roads.

2 Methodology

The methodology for appending high-precision elevation data to GPS data is divided into two 

processes: 1) the two-dimensional GPS coordinates are used to query a DEM, and 2) the 

resultant elevations are filtered to remove anomalous data and smoothed to produce stable road 

grade estimates.

2.1 Elevation Lookup

The premier DEM of the contiguous United States is widely considered to be maintained by the 

U.S. Geological Survey (USGS) (see Figures 1 and 2 for visual representations of the USGS 

DEM nationwide and the state of Colorado, respectively). Available in multiple resolutions, the 

1/3-arc-second scale is employed herein as it is the highest resolution version that provides 

defined static elevation values for the entire continguous United States at approxomately 10-

meter intervals (resulting in over 100 billion data points). In addition to its extensive coverage, 

the accuracy of the USGS DEM has been validated against a series of survey-quality data

elevation markers with a reported root mean square error of 2.44 meters [32]. For further 

documentation on the USGS DEM, see [33, 34]. 

Figure 1. Elevation map of the contiguous United States produced using the USGS DEM
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Figure 2. Elevation map of the state of Colorado produced using the USGS DEM

While the extent and accuracy of the USGS DEM make it an extremely powerful tool, 

consideration must be taken to house and query the database in an efficient manner. The USGS 

DEM is organized into a rectangular array of grid cells by geographic region with each directory 

containing multiple data files for sub-regions within the larger grid cell. When querying the 

DEM, the raw GPS coordinates are first converted into the World Geodetic System 84 

geographic coordinate system [35] coincident with the DEM. Next, the point data are surveyed to 

identify the unique file locations for all grid cells traversed. Having identified the relevant file 

locations for an individual GPS trace, the data are reordered by grid cell to avoid multiple 

queries to an individual geographic region. Organizing the GPS data by grid cell maximizes 

computational resources by minimizing calls to the DEM. Elevation values for each grid cell are 

then extracted from the DEM in raster format, resorted according to the original GPS data, and 

appended to the database coincident with the appropriate source data. 

It is important to note that the USGS DEM is a “bare-earth” dataset (as opposed to “top of 

canopy” DEMs) and as such, generally returns the lowest elevation at a given point. For instance, 

at river/bridge and highway/overpass intersections, the USGS DEM will return the lower of the 

two elevations (see Figure 3 for several examples of discontinuous intersections from downtown 

Denver, Colorado, where the USGS DEM is inlaid with maps and satellite imagery from 

Google). When matched to two-dimensional GPS coordinates from a vehicle speed trace, the 

USGS DEM returns sudden drops (and subsequent returns) in elevation of tens of feet. In the 

absence of additional processing, these sudden elevation changes would result in 

misrepresentative road grade values that would adversely affect subsequent calculations of drive 

cycle intensity and related fuel economy. In the next section, we discuss processing routines

developed to identify such occurrences and filter elevation profiles accordingly. 
4 

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Figure 3. Coincident maps of downtown Denver, Colorado, produced using the USGS DEM, 

Google Maps Satellite layer, Google Maps Streets layer, and Google Maps Hybrid layer

(Google Maps credit: © 2014 Google, Map Data © 2014 Tele Atlas)

2.2 Data Filtration

After querying the DEM, raw elevations are adjusted using a multi-step filtration routine. This 

process seeks to remove errant elevation data associated with segments of elevated roadway

(such as bridges and overpasses) and create smooth elevation profiles that result in continuous 

road grade signals for vehicle simulation. Parallels exist between these elevation filtration 

techniques and existing National Renewable Energy Laboratory algorithms for the filtration of 
5 

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vehicle speed traces from GPS data [36]. The multi-step elevation filtration routine is outlined in

five steps with corresponding images in Table 1. 

Table 1. Step-by-Step Example of Elevation Filtration/Smoothing Performed on Sample Roadway

Step A: Raw elevation values 

versus distance.

Step B: Elevation data are 

downsampled into uniformly 

spaced intervals, with each point 

representing the median value.

Step C: Downsampled data are 

passed through a combined 

Savitzky-Golay and binomial filter

(attenuating high frequncy noise), 

and the difference between prefiltered and post-filtered elevation 

values are computed.

Step D: Points where the 

elevation difference resulting from 

filtration exceeds a given value are 

discarded and backfilled via 

interpolation.

Step E: The backfilled elevation 

profile is passed through the 

aforementioned combined 

Savitzky-Golay and binomial filter

to eliminate noise from the 

distance derivative. Elevations at 

the orignal distance values are 

calculated via interpolation.

After reviewing the elevation filtration process in great detail, we now highlight the net impact of 

the routine by examining the example raw versus filtered elevation and grade profiles in 

Figure 4. This plot highlights the two primary functions of the filtration routine: 1) the removal 

of errant data points, and 2) data smoothing. Errant data points are easily identified through 
6 

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visual inspection of elevation profiles and are programatically identified via the filtration 

algorithm. Left unchanged, these dramatic drops in elevation would result in unrealistic grade 

values that are unsuitable for downstream vehicle simulation programs (instantaneous maximum 

power request from propulsion/braking system, inability of vehicle to maintain desired speed, 

potential for simulation results to be invalidated, etc.). While less visually apparent in the trace of 

raw elevation versus distance, the inherent noise for the duration of the raw road grade signal 

would result in unrealistic powertrain behavior were it attempted to be met as part of the drive 

cycle during powertrain simulation. Elevation smoothing removes such noise and provides stable 

grade signals.

Figure 4. Raw versus filtered USGS elevation and road grade data

While the importance of elevation filtration has been highlighted in this section, particularly as it 

relates to vehicle powertrain simulation, we note that it generally does not have a 

transformational effect on the base layer USGS data. Over a representative sample of 53 million 

filtered elevation points from the National Renewable Energy Laboratory’s Transportation 

Secure Data Center [37], 79% of the elevation values were adjusted by less than one foot and 

96% of the elevation values were adjusted by less than five feet.
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3 Validation

To evaluate the accuracy of this procedure for calculating road grade, we compare the results of 

our DEM-based road grade estimation with the Navteq/Nokia/HERE ADAS height/slope 

database of elevation and road grade values for approximately five million points in the 

contiguous United States [38]. The ADAS height/slope layer is a commercial data product 

containing road grade values for the majority of U.S. highways and select low capacity 

roadways. By validating our methods to roadways where the ADAS data have coverage, we 

expect to establish a reasonable level of confidence in our ability to estimate grade on all 

roadways. 

For each point in the ADAS data, the corresponding links in the Navteq Streets layer are selected 

and used to populate a list of road-matched coordinates surrounding the selected point in both 

directions (if possible). These coordinates are then used to perform a lookup on the USGS DEM 

to append raw elevation values. These raw values are then filtered using the methods described 

in Section 2.2. Having both elevation and road grade data from the ADAS dataset and our 

filtered USGS DEM, the degree of agreement between these two data products can be evaluated. 

This evaluation will be presented in two sections with the first inspecting a short example section 

of roadway and the second contrasting the two datasets across large aggregations of data. 

3.1 Example Roadway

First, we will examine an example section of roadway to compare filtered USGS values against 

ADAS data (see Figure 5). Inspection of the two elevation profiles and their associated 

derivatives reveals that while the general shapes of the filtered USGS and ADAS elevation 

profiles are similar, the filtered USGS elevation values exhibit a constant offset of approximately 

one hundred feet when compared to the ADAS dataset. The strong correlation in derived road 

grade coupled with the constant offset in elevation values suggests the disagreement in elevation 

can be attributed to the application of dissimilar global datums when determining absolute 

elevation [39–41]. Constant elevation offsets between readings from two different GPS devices 

are quite common, as each manufacturer will often use its own internal methodology for 

projecting elevation measurements from a global datum representing the sea level of the earth 

[42–43]. Such an offset, while significant in terms of absolute elevation, has no bearing on the 

calculation of road grade because it is defined as the derivative of the elevation with respect to 

distance traveled and is representative of the shape or profile of the data.

The lower graph in Figure 5 shows the absolute value of road grade as calculated from the 

filtered USGS elevation profile versus equivalent values from the ADAS dataset. While road 

grade is available as a signed value in both the USGS and ADAS datasets, comparisons between 

the two are made in terms of absolute values. The decision to perform the comparison on 

absolute values of road grade was made to limit user interpretation of direction of travel and its 

associated bias, and instead have the comparison focus on statistical trends in the underlying 

data. Given the large sample size of the dataset, any error introduced as a result of this decision is 

minimized due to the law of large numbers affixed to the central limit theorem. For the example 

road profile shown here, road grade values generally agree very well between the two datasets.
8 

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Figure 5. Sample elevation and road grade (absolute value) signals with filtered USGS data plotted 

as a red line and ADAS height/slope data overlaid as blue markers

3.2 Aggregate Comparisons

While example comparisons are useful in terms of disclosing comparison methods and results at 

the lowest level, larger aggregations of data are necessary to more broadly quantify the 

agreement between the USGS and ADAS datasets. To that end, the two data sets are segregated 

by road type and cumulative distributions of road grade are plotted for each (see Figure 6). Road 

type are classified using Navteq’s definition of “functional class” where Functional Class 1 roads 

exhibit generally higher volumes and speeds and Functional Class 4 roads generally exhibit 

lower volumes and speeds. Table 2 presents more thorough definitions of the various functional 

classes.
9 

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Table 2. Navteq-Defined Road Functional Classes and Descriptions 

Functional Class Description 

1 Roads with very few, if any speed changes, typically controlled 

access, and provide high volume, maximum speed movement 

between and through major metropolitan areas.

2 Roads with very few, if any speed changes, and provide high volume, 

high speed traffic movement. Typically used to channel traffic to (and 

from) Level 1 roads.

3 Roads which interconnect Level 2 roads and provide a high volume of 

traffic movement at a lower level of mobility than Level 2 roads.

4 Roads that provide for a high volume of traffic movement at moderate 

speeds between neighborhoods.

5 All other roads.

Figure 6. Cumulative distribution of road grade by functional class 
10 

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A few observations from Figure 6 include:

• The ADAS dataset contains more points on Functional Class 2 and 4 roads than on 

classes 1 and 3. A count of roadways by functional class in the United States reveals that 

as the functional class increases, so does the number of roads (i.e., the majority of roads 

are low speed and capacity). Additionally, Navteq self-reports to have near 100% 

coverage of Functional Classes 1 and 2 in the ADAS dataset, while Functional Classes 3 

and 4 are well below 50% coverage, and no data is available for Functional Class 5. 

• The slope of the curves reveals that Functional Class 1 and 2 roads have a smaller share 

of data at steep road grades as compared to classes 3 and 4. 

• The level of agreement between the filtered USGS and ADAS data is relatively strong, 

with the filtered USGS data generally exhibiting a slightly higher concentration of points 

at steep road grades. A chi-squared test reveals that the filtered USGS and ADAS 

distributions are samples of the same underlying distribution with a likelihood of 

>99.9%. 

After examining the data by road type, the two datasets are next aggregated by geography. The 

cumulative distributions of road grade can be examined by state (see Figure 7). Five states, 

California, Colorado, Texas, Florida, and New York, are selected for their diverse distributions 

of road grade and relatively high volume of data. 

Figure 7. Cumulative distribution of road grade by geography 
11 

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A few observations from Figure 7 include: 

• The ADAS dataset contains more points for the states of California, Texas, and New 

York compared to Colorado and Florida (a trend mirrored by the size of the total road 

networks in each state).

• The slope of the cumulative distribution curves reveals that the states of California, 

Colorado, and New York tend to exhibit higher concentrations of steep road grade than 

the states of Texas and Florida.

• The level of agreement between the filtered USGS and ADAS data is relatively strong, 

with the filtered USGS data generally exhibiting a slightly higher concentration of points 

at steep road grades. A chi-squared test reveals that the filtered USGS and ADAS 

distributions are samples of the same underlying distribution with a likelihood of 

>99.9%. 

While these cumulative distributions of road grade are encouraging in that the two datasets 

appear to contain similar trends with respect to road type and geography, a more rigorous 

comparison evaluating the distributions of road grade disagreement on a point-by-point basis is 

warranted. This comparison is presented in Figure 8, where distributions of road grade error by 

ADAS-reported road grade for Functional Class 1 roads are shown (similar distributions are 

observed in the data for Functional Classes 2 through 4 and therefore are omitted). 

For the purpose of illustration, let us identify and describe two arbitrary points on this plot. 

Consider a marker existing in the ADAS grade bin of 0% with a filtered USGS error of +1.0%. 

Such a marker would have an ADAS-reported road grade with absolute value between 0% and 

0.5% and a filtered USGS grade 1.0% steeper than the ADAS-reported value (overestimating 

road grade by 1.0%). Another example would be a point in the ADAS grade bin of 5% with a 

filtered USGS error of -2.0%. This point corresponds to data with an ADAS grade absolute value 

between 4.5% and 5.5% and a filtered USGS grade 2.0% less steep than the ADAS-reported 

value. 

Having interpreted the layout of this plot, a few observations come to light: 

• In terms of median value and interquartile range, the filtered USGS data tend to 

underestimate grade (more often than it overestimates) on grades steeper than 1% and 

tends to overestimate (more often than it underestimates) on grades less than 1% (all 

relative to ADAS data).

• The variance of each distribution tends to increase with grade.

• Extreme outliers are almost exclusively found in the overestimation region, a byproduct 

of the assumption that the filtered USGS data results in the correct sign for the estimated

road grade (i.e., assuming the correct sign, it is impossible to underestimate a 3% grade 

by more than 3% grade). 

• Outlier density stands out at low ADAS grades due to the overall high density of data at 

low grade values (i.e., the majority of points exist at low grade values). 
12 

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Figure 8. Distribution of road grade estimation error by ADAS road grade for Functional Class 1 

roads 

(Additional statistics included as text: point count, outlier point count, median, interquartile range) 

It is worth noting that when taken in aggregate, median values for filtered USGS error are very 

nearly equal to zero for all functional classes of roadway. 

While the agreement between the filtered USGS and ADAS datasets is quite good, there are 

certain instances of disagreement. Such instances are suspected to stem from one of the 

following sources: 

• Erroneous measurements in the ADAS dataset

• Erroneous measurements in the USGS DEM

• Mistaken selection of two-dimensional coordinates leading up to ADAS points 

• Limitations of filtration techniques (i.e., unintended filtration of good points or missed 

filtration of bad points).

In aggregate, over the millions of data points for which filtered USGS road grade was compared 

to the ADAS dataset, the aggregate root mean square error was 1.48% road grade. 
13 

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4 Summary

A validated approach for appending high-precision elevation and road grade data to a series of 

GPS coordinates has been presented. A robust methodology for querying a static DEM and 

filtering/smoothing the resultant elevation profiles has been outlined. This methodology seeks to 

eliminate instances of sudden drops (and subsequent returns) in elevation and to dampen high 

frequency content in order to produce stable derivative signals of road grade. The agreement 

between the proposed method and a commercially available database of road grade has been 

quantified in several dimensions, including by road type, geography, and grade. Over millions of 

data points, the aggregate root mean square error of the presented method was found to be 1.48% 

road grade. 

It has been demonstrated that road grade data can be extracted from the USGS DEM with a 

strong level of agreement to the commercially available ADAS height/slope data layer at the 

national level. While acknowledging the commercial value of the ADAS data, the USGS DEM 

provides the distinct advantages of being freely available as open data and having complete 

coverage over the contiguous United States and all roadways contained therein. This work is 

expected to be a valuable tool for researchers and engineers seeking to increase the fidelity of 

their work in the estimation of real-world fuel economy via modeling, simulation, and analysis. 
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